Influence functions of trimmed likelihood estimators for lifetime experiments
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Date
2015
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Abstract
We provide a general approach for deriving the influence function for trimmed
likelihood estimators using the implicit function theorem. The approach is applied
to lifetime models with exponential or lognormal distributions possessing a linear
or nonlinear link function. A side result is that the functional form of the trimmed
estimator for location and linear regression used by Bednarski and Clarke (1993,
2002) and Bednarski et al. (2010) is not generally always the correct functional form
of a trimmed likelihood estimator. However, it is a version for which the influence
function has a treatable form. A real data example shows the effect of trimming using
a nonlinear link function for either the exponential or lognormal distribution.
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Keywords
outlier robustness, lifetime distribution, generalized linear model, robust estimation